A Short Note on Lyapunov Type Inequalities for Hilfer Fractional Boundary Value Problems

This paper deals with fractional boundary value problems involving the Hilfer fractional differential operator of order $1 < \alpha \leq 2$ and type $0 \leq \beta \leq 1$. We derive the corresponding Lyapunov-type inequalities for two prominent classes of Hilfer fractional boundary value problems (HFBVPs) involving separated and anti-periodic boundary conditions. For this purpose, we construct the associated Green's functions and deduce their important properties.